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A224342
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Apparently solves the identity: find sequence B that represents the numbers of ordered compositions of n using the terms of A, and vice versa.
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2
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1, 2, 3, 6, 10, 18, 32, 57, 101, 179, 318, 564, 1002, 1778, 3157, 5604, 9949, 17661, 31352, 55657
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OFFSET
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1,2
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COMMENTS
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It appears that given any sequence of real numbers taken out of a hat, S(n); repeated iterates of the operation: S(n) -> characteristic function of S(n) -> INVERT transform of the latter -> new sequence, then (repeat), will converge upon two sequences A = A224341 and B = A224342 as a 2-cycle fixed limit.
Alternatively as a conjecture, A and B solve the unique identity as described in the heading as to ordered compositions with A = A224341 and B = A224342. The INVERT transform of the characteristic function of A = B, and the INVERT transform of the characteristic function of B = A.
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LINKS
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FORMULA
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Repeated trials of any sequence of real numbers pulled out of a hat will apparently converge upon A224341 and A224342 as a 2-cycle fixed limit (absolute values of terms). There is no known generating function at the date of this submission.
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EXAMPLE
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Given the sequence (1, 0, 0, 0, ...) and following the iterative rules, the sequences converge upon A224341 and A224342 as an alternating fixed limit.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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